Abstract
Relaxation-fluctuation theory is developed for the single-particle distribution function of a classical fluid. Fictitious potentials coupling to arbitrary functions of the internal variables are used to extract equilibrium correlation functions from kinetic equations. In particular the autocorrelation function in the microscopic quantity related to the single-particle distribution is studied. Two procedures are developed for the calculation of this function. To lowest order they both result in the same approximate equation of motion. The first procedure assumes a linear functional dependence on the density of the collision term in the exact equation of motion. The second uses a set of variational eigenfunctions of the Liouville operator which were introduced by Zwanzig. The resulting equation of motion is an effective field equation which had been proposed phenomenologically by one of the authors in an earlier paper.
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